1. Field of the Invention
This invention relates generally to electrokinetic fluidic devices, and in particular to the use of non-Newtonian liquids in electrokinetic fluidic devices.
2. Background of the Invention
Electrokinetic, or electroosmotic, flow is a well-known phenomenon. An electrokinetic fluidic (EOF) device typically includes a liquid-filled conduit that has an inlet and an outlet and may also contain porous material. The interior wetted surfaces of the conduit and any material disposed within the conduit display a zeta potential, which describes an electrical potential that exists across the interface between the conduit and the wetting fluid. In use, an electrical potential difference and/or a fluidic pressure-difference are applied between the inlet and the outlet.
A key parameter used to characterize an electrokinetic device is the electroosmotic mobility, which is given according to the classical Helmholtz-Smoluchowski formula as the product of the zeta potential and the liquid dielectric permittivity divided by the liquid dynamic viscosity.
Another key parameter is the Debye length in the liquid. The liquid in an electrokinetic device is ironically conducting due to the presence of some concentration of ionic particles in the liquid. The ionic particles can be any combination of salts or buffers that are fully dissolved or partially dissolved in the liquid. The combination of ionic particles is characterized by an ionic strength. The Debye length is inversely proportional to the square root of this ionic strength. In water at ambient temperature, for example, the Debye length is about 13.6 nanometers divided by the square root of the ionic strength, with ionic strength taken in units of millimoles per liter.
A third key parameter is the effective inside diameter of the conduit, called the pore scale. For a conduit of irregular cross-sectional shape, a conduit that contains sections that are subdivided (e.g., a bundle of capillaries), or a conduit that contains sections of porous material, a method for determining the pore scale is described in Johnson et al. [D. L. Johnson, J. Koplik and R. Dashen, “Theory of dynamic permeability and tortuosity in fluid-saturated porous media,” F. Fluid Mech. vol. 176 pp. 379-402 (1987).].
For conditions where the pore scale is substantially greater than the Debye length (e.g., the pore scale is more than 100 times larger than the Debye length), the electroosmotic flow can be treated as ideal. For ideal electroosmotic flow, the electroosmotic mobility may be given by the classical Helmholtz-Smoluchowski formula. But where the pore scale is less than about 100 times the Debye length, several non-ideal processes become important: (1) The electroosmotic mobility is reduced; (2) The electrical conductivity of the liquid within the conduit is increased; and (3) Electrical conduction and electroosmosis pro flux through the conduit that causes a reduction of ionic concentration at the inlet of the conduit, which is inherently unstable. These non-ideal effects are amplified as the zeta potential is increased and/or the pore scale is decreased.
To maximize the classical electroosmotic mobility, the electrokinetic arts teach the use of a high zeta potential with liquids that have a high ratio dielectric permittivity per dynamic viscosity. Under ideal conditions, the volumetric flow rate produced by an electrokinetic device is equal to the electric current through the conduit times the electroosmotic mobility divided by the electrical conductivity of the liquid. The maximum pressure (e.g., the stall pressure) produced by an electrokinetic device is then equal to 32 times the electroosmotic mobility times the liquid dynamic viscosity times the voltage applied across the device divided by the square of the pore scale of the device.
A liquid that displays a linear and proportional relationship between shear stress and shear rate is called a Newtonian liquid. For a Newtonian liquid, the shear stress is equal to the product of shear rate and liquid dynamic viscosity. Traditional electrokinetic devices use Newtonian liquids. Because Newtonian liquids have a constant ratio of shear stress to shear rate, the viscosity of the liquid under electroosmotically driven conditions is equal to that under pressure driven conditions. In classical electroosmotic devices, therefore, both the electroosmotic-and pressure-driven flow rates are inversely proportional to the same liquid viscosity.
In many practical applications, electrokinetic devices are designed to produce flow through some external flow resistance, which allows them to produce flow of a fluid against a backpressure. This has been accomplished by balancing the use of small pore size to provide a high stall pressure (hence the need to increase ionic strength to avoid non-ideal effects) against reducing ionic strength to minimize the current required to provide flow. High current is preferably avoided to avoid Joule-heating that can lead to thermal runaway and to reduce electrochemical evolution of the liquid at the electrodes that are positioned at the terminal ends of the electrokinetic device.